BEGIN:VCALENDAR VERSION:2.0 PRODID:-//University of Utah Math Department//Commutative Algebra Seminar//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-WR-CALNAME:Commutative Algebra Seminar - Fall 2018 X-WR-CALDESC:Commutative Algebra Seminar at University of Utah Mathematics Department X-WR-TIMEZONE:America/Denver BEGIN:VEVENT UID:20180824T143000-michael-brown@math.utah.edu DTSTART;TZID=America/Denver:20180824T143000 DTEND;TZID=America/Denver:20180824T153000 DTSTAMP:20260824T165229Z SUMMARY:Chern-Weil theory for matrix factorizations DESCRIPTION:Speaker: Michael Brown\, University of Wisconsin, Madison\n\nThis is a report on joint work with Mark Walker. Classical algebraic Chern-Weil theory provides a formula for the Chern character of a projective module P over a commutative ring in terms of a connection on P. In this talk, I will discuss an analogous formula for the Chern character of a matrix … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20180831T143000-ben-briggs@math.utah.edu DTSTART;TZID=America/Denver:20180831T143000 DTEND;TZID=America/Denver:20180831T153000 DTSTAMP:20260824T165229Z SUMMARY:Lusternik-Schnirelmann category in commutative algebra DESCRIPTION:Speaker: Ben Briggs\, University of Utah\n\nL-S category is a numerical invariant originating in differential geometry, which has since found an important place in rational homotopy theory. In the early 80s commutative algebraists and rational homotopy theorists began to uncover deep parallels between their disciplines, greatly enriching both … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20180907T143000-thomas-polstra@math.utah.edu DTSTART;TZID=America/Denver:20180907T143000 DTEND;TZID=America/Denver:20180907T153000 DTSTAMP:20260824T165229Z SUMMARY:Prime characteristic invariants and birational maps DESCRIPTION:Speaker: Thomas Polstra\, University of Utah\n\nWe explore the behavior of prime characteristic invariants, such as F-signature and Hilbert-Kunz multiplicity, under birational morphisms. We will discuss both positive and negative behavior. LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20180914T143000-jenny-kenkel@math.utah.edu DTSTART;TZID=America/Denver:20180914T143000 DTEND;TZID=America/Denver:20180914T153000 DTSTAMP:20260824T165229Z SUMMARY:Local cohomology of thickenings DESCRIPTION:Speaker: Jenny Kenkel\, University of Utah\n\nLet R be a standard graded polynomial ring that is finitely generated over a field, and let I be a homogenous prime ideal. Bhatt, Blickle, Lyubeznik, Singh, and Zhang examined the local cohomology of R/I^t, as t goes to infinity, which led to the development of an asymptotic invariant by Dao and … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20180921T143000-henning-krause@math.utah.edu DTSTART;TZID=America/Denver:20180921T143000 DTEND;TZID=America/Denver:20180921T153000 DTSTAMP:20260824T165229Z SUMMARY:The Morita theory for derived categories revisited DESCRIPTION:Speaker: Henning Krause\, University of Bielefeld\n\nA fundamental theorem of Rickard states for a pair of coherent rings that the categories of perfect complexes are triangle equivalent if and only if their bounded derived categories of finitely presented modules are triangle equivalent. The proofs of both directions are somewhat delicate and not … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20181005T143000-rebecca-r.g.@math.utah.edu DTSTART;TZID=America/Denver:20181005T143000 DTEND;TZID=America/Denver:20181005T153000 DTSTAMP:20260824T165229Z SUMMARY:Characteristic-free test ideals DESCRIPTION:Speaker: Rebecca R.G.\, George Mason University\n\nWe define the test ideal of a general closure operation cl, and give some of its properties. We highlightconnections to the trace ideal and interior operations, and the applications of these viewpoints to the study of singularities of commutative rings. In all characteristics, test ideals coming … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20181026T143000-cris-negron@math.utah.edu DTSTART;TZID=America/Denver:20181026T143000 DTEND;TZID=America/Denver:20181026T153000 DTSTAMP:20260824T165229Z SUMMARY:Cohomology for finite tensor categories and some fundamental operations DESCRIPTION:Speaker: Cris Negron\, M.I.T., Boston\n\nThis talk concerns the finite generation conjecture for finite tensor categories. One is free to think only of representation categories of finite-dimensional Hopf algebras here. The conjecture proposes that for any finite tensor category C, the self-extension algebra of the unit is a finitely … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20181109T143000-linquan-ma@math.utah.edu DTSTART;TZID=America/Denver:20181109T143000 DTEND;TZID=America/Denver:20181109T153000 DTSTAMP:20260824T165229Z SUMMARY:Kunz's theorem in ALL characteristics DESCRIPTION:Speaker: Linquan Ma\, Purdue University\n\nIn the 1970s Kunz proved that a Noetherian ring of positive characteristic is regular if and only if the Frobenius is flat. I will discuss various extensions of this theorem. Then I will give a version of Kunz's theorem in mixed characteristic (joint with Bhatt and Iyengar), and a version in … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20181116T143000-lars-winther-christensen@math.utah.edu DTSTART;TZID=America/Denver:20181116T143000 DTEND;TZID=America/Denver:20181116T153000 DTSTAMP:20260824T165229Z SUMMARY:An Ideal Solitaire Puzzle DESCRIPTION:Speaker: Lars Winther Christensen\, Texas Tech., Lubbock\n\nTwo algebraic varieties are said to be linked if their union is a particularly nice kind of variety, a complete intersection. Thus, linked varieties are in some sense complementary: one carries an imprint of the other. Linkage has an algebraic incarnation that is used to study ideals. In the talk I … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20181130T143000-robert-m.-walker@math.utah.edu DTSTART;TZID=America/Denver:20181130T143000 DTEND;TZID=America/Denver:20181130T153000 DTSTAMP:20260824T165229Z SUMMARY:On ideals defining products of affine schemes DESCRIPTION:Speaker: Robert M. Walker\, University of Michigan\n\nThis is joint work with Irena Swanson found on arXiv:1806.03545. Given a polynomial ring C over a field and proper ideals I and J whose generating sets involve disjoint variables, we determine how to embed the associated primes of each power of I+J into a collection of primes described in terms of … LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT BEGIN:VEVENT UID:20181207T143000-patrick-graf@math.utah.edu DTSTART;TZID=America/Denver:20181207T143000 DTEND;TZID=America/Denver:20181207T153000 DTSTAMP:20260824T165229Z SUMMARY:TBA DESCRIPTION:Speaker: Patrick Graf\, University of Utah\n\nTBA LOCATION:LCB 215 URL:http://math.utah.edu/caseminar/2018-fall/ END:VEVENT END:VCALENDAR